Advanced Statistics: Theory and Methods

This course covers fundamental concepts in probability, statistical theory, and methodology. Topics include probability distributions, multivariate normal distributions, transformations, sampling distributions, principles of inference (including Bayesian inference), maximum likelihood estimation, goodness-of-fit tests, likelihood ratio, significance testing, linear models and least squares, generalized linear models, model selection, and nonparametric density estimation. Python is used for data-analytic applications.

The course begins with probability models, transformations, and sampling distributions before introducing the principles of statistical inference, including estimation and hypothesis testing. Building on these foundations, students explore modelling and inference for complex datasets using significance testing, confidence intervals, bootstrap methods, linear and generalized linear models, Bayesian inference, model assessment, model selection, and nonparametric estimation. The course combines statistical theory with computational methods and data-analytic applications using Python.

Upon successful completion of this course, students will be able to:

• Simulate sampling distributions and verify the Weak Law of Large Numbers (WLLN) and Central Limit Theorem (CLT).
• Compute estimators using different statistical techniques and compare their performance.
• Derive and evaluate hypothesis tests for different parameters using analytical and computational methods.
• Analyse complex datasets using statistical methods while identifying the strengths and limitations of different approaches.
• Compare statistical and computational methods for data analysis.
• Design a complete statistical workflow for solving a data-driven problem, including experimental design, data collection, exploratory analysis, hypothesis testing, modelling, and interpretation of results.

• Foundations of Statistics for Data Scientists: With R and Python – Agresti, A. and Kateri, M.
• Fundamentals of Probability and Statistics for Machine Learning – Ethem Alpaydin.
• Statistical Inference – George Casella and Roger L. Berger.
• An Introduction to Statistical Data Science: Theory and Methods – Giorgio Picci.
• Probabilistic Machine Learning: An Introduction – Kevin P. Murphy.
• Introduction to Probability, Statistics & R: Foundations for Data-Based Sciences – Sujit K. Sahu.

Not available.

What will I learn in this course?

You will learn advanced statistical theory and computational methods, including probability models, statistical inference, hypothesis testing, regression models, Bayesian inference, model selection, and nonparametric estimation, with applications in data science and machine learning.

Does the course include programming?

Yes. Python is used for data-analytic applications throughout the course.

What are the prerequisites?

Students are expected to have completed Math of Uncertainty and Introduction to Data Science before taking this course.

How is the course assessed?

Assessment includes two examinations, quizzes, assignments, and attendance with class participation.